I have a female dog, does that make me, like, lesser of a guy?
No, of course not. It makes that person's opinion matter lesser now to you, as that's ignorant macho-bullshit thinking usually indicative of insecurity in addition to a lack of intelligence.
Someone brought it to my attention, that I should have a dog with nuts,
What a foolish thing to opine. Also, unless you're a professional dog breeder, it's cruel not to fix your dog while depriving them of sex. It's also unhealthy and can cause an animal to develop testicular cancer, or ovarian cancer for females.
I didn't think this was a thing..
Oh it is. That same kind of person often thinks it's unmanly to have only daughters and no sons, as if masculinity could be measured in one's propensity to have male offspring. Clearly this is the opinion of someone who doesn't understand genetics and is all too happy to share this idiotic view with the world around them.
Are guys only allowed to have male dogs?
I really shouldn't even answer this as you know the answer already. Anyone who would think less of you for owning a female dog instead of a male dog has a moronic and immature view of this topic. The only approval you need is from the man in the mirror.
Only to insecure people who try to mask this with cringe-worthy arrogance, entitlement, arbitrary projection and a cartoonishly over-masculinized, insufferable, macho attitude.
Don't be. Some people were taught stupid shit growing up. Generally, the female of most mammalian species will exhibit somewhat more docile behavior, which is generally what humans look for in dogs, that plus intelligence, companionship, and protection of the homefront. Trust me, female dogs don't slack on being useful as watch dogs. Don't feel lost and don't listen to that foolishness.